Maximal regularity for parabolic partial differential equations on manifolds with cylindrical ends

TL;DR

This paper presents a simplified proof of maximal regularity for linear parabolic PDEs on manifolds with cylindrical ends, utilizing pseudodifferential parametrices and R-boundedness of the resolvent.

Contribution

It introduces a streamlined approach to establish maximal regularity on manifolds with cylindrical ends using advanced pseudodifferential techniques.

Findings

Proof of maximal regularity using pseudodifferential parametrices

Application of R-boundedness for the resolvent in PDE analysis

Simplification of existing proofs for parabolic equations on complex manifolds

Abstract

We give a short, simple proof of maximal regularity for linear parabolic evolution equations on manifolds with cylindrical ends by making use of pseudodifferential parametrices and the concept of R-boundedness for the resolvent.